Abstract In this study, we present an immersed boundary reconstruction method for the simulation of viscous compressible flows presenting strong discontinuities in the vicinity of the immersed body. The technique we propose is based on a weighted least-square reconstruction. Its major feature is that the weights are automatically adapted to the presence of a discontinuity within the least-square stencil by using a shock-sensor approach. In so doing, the reconstruction becomes ENO-like and mathematically consistent even in the presence of strong discontinuities. The objective of this paper is to demonstrate that it then becomes possible to use an immersed boundary method for the simulation of hypersonic flows and that it is robust, even for flows around complex geometries. To do so, two-dimensional compressible Navier-Stokes equations are solved to study canonical hypersonic flows and it is showed that the results are in good agreement with either experimental data and/or body-fitted approaches and that the impact of the immersed boundary technique on the overall spatial order of convergence is reasonable.

中文翻译：

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使用类 ENO 最小二乘重建的高超声速流动的浸入边界条件

摘要 在这项研究中，我们提出了一种浸入边界重建方法，用于模拟在浸入体附近呈现强烈不连续性的粘性可压缩流。我们提出的技术基于加权最小二乘重建。它的主要特点是通过使用震动传感器方法，权重会自动适应最小二乘模板内不连续性的存在。这样做时，即使在存在强烈不连续性的情况下，重建也变得类似于 ENO 并且在数学上是一致的。本文的目的是证明使用浸入边界方法模拟高超音速流动成为可能，并且即使对于复杂几何形状周围的流动，它也具有鲁棒性。为此，